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Fig. 1.12. Left Euler-Lagrange tensor, K 1 > 0 ,K 2 > 0, left Euler-Lagrange circle
S 1 , left Euler-Lagrange
ellipse
E 1 K 1 , K 2
S 1 , left Euler-Lagrange
Fig. 1.13. Left Euler-Lagrange tensor, K 1 > 0 ,K 2 < 0, left Euler-Lagrange circle
H 1 K 1 , K 2
hyperbola
, left and right focal points F l and F r
Fig. 1.14. Right Euler-Lagrange tensor, κ 1 > 0 2 > 0, right Euler-Lagrange circle
S 1 , right Euler-Lagrange
E 1 K 1 , K 2
ellipse
Corollary 1.9 (Relation between the Cauchy-Green and the Euler-Lagrange deformation tensor).
2E l =J l G r J l
J r G l J r =G r
G l =C l
G l
2E r =G r
C r
versus
versus
versus
C l =2E l +G l ,
C r =G r 2E r ;
(1.120)
E l =J l E r J l
versus E r =J r E l J r ;
2 K i = Λ i ∀i =1 , 2
versus 2 κ i = λ i 1 ∀i =1 , 2 .
End of Corollary.
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